Chapter 1 Flashcards
Definition of a function
a function f from a set A to a set B is a relations that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain of the function and the set B is the range of the function
What are the 4 ways to represent a function?
verbally, numerically, graphically, algebraically
The set of all numbers where the function is defined is called the domain. What are the two main ways functions are undefined?
when the denominator equals zero or an even root contains a negative value inside
difference quotient
f(x+h) - f(x) / h
slope intercept form
y = mx + b
slope
rise/run = y2-y1/x2-x1
point slope form
y - y1 = m (x-x1)
parallel lines, slopes are ___
same
perpendicular lines, slopes are____
negative reciprocals
distance formula
the square root of (x2-x1)^2 + (y2-y1)^2
midpoint formula
(x1+x2)/2, (y1+y2)/2
equation of a circle
(x-h)^2 + (y-k)^2 = r^2
how to find x intercept
let y=0, solve for x
how to find y intercept
let x=0, solve for y
how to test for x-axis symmetry
plug in “-y” for y and see if same
how to test for y-axis symmetry
plug in “-x” for x and see if same
how to test for origin symmetry
plug in “-x” for x and “-y” for y and see if same
find zeros of a function
let f(x) = 0
how to find rate of change
it is the same as slope
how to test for even function
plug “-x” into f(x)
how to test for odd function
plug “-x” into f(x)
even functions are symmetric to _____
y axis
odd functions are symmetric to _____
the origin
f o g
f(g(x))
g o f
g(f(x))
g o g
g(g(x))
how to verify that 2 functions are inverses
show that f(f^-1(x)) - x AND f^-1(f(x)) = x, therefore (3 dots) f and f^-1 are inverses
